No. You can only define autonomous transactions at the top-level declaration of anonymous blocks:

create table t (
  c1 int
);

declare
  pragma autonomous_transaction;
begin
  insert into t values ( 1 );
  commit;
end;
/

begin
  declare
    pragma autonomous_transaction;
  begin
    insert into t values ( 2 );
    commit;
  end;
end;
/

PLS-00710: Pragma AUTONOMOUS_TRANSACTION cannot be specified here

begin
  raise zero_divide;
exception
  when zero_divide then
    declare
      pragma autonomous_transaction;
    begin
      insert into t values ( 3 );
      commit;
    end;
end;
/

PLS-00710: Pragma AUTONOMOUS_TRANSACTION cannot be specified here

select * from t;

C1   
   1 

If you need a separate transaction in your exception handler (e.g. for error-logging), define the autonomous transaction in a procedure. And call that.